Semiconductor process modeling system and method

ABSTRACT

Provided is a semiconductor process modeling system. The semiconductor process modeling system includes a preprocessing component configured to generate tensor data from raw data obtained from semiconductor manufacturing equipment, wherein, when the raw data is expressed as a raw matrix representing values of a plurality of process parameters for each of a plurality of wafers, at least one element of the raw matrix is omitted, when the tensor data is expressed as a tensor matrix representing values of a plurality of preprocessed process parameters for each of the plurality of wafers, the number of omitted elements of the tensor matrix is less than the number of omitted elements of the raw matrix, and the preprocessing component is configured to generate the tensor data by modifying the raw data based on at least one of characteristics of the semiconductor manufacturing equipment and characteristics of the plurality of process parameters.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based on and claims priority under 35 U.S.C. § 119to Korean Patent Application No. 10-2021-0089329, filed on Jul. 7, 2021,in the Korean Intellectual Property Office, the disclosure of which isincorporated by reference herein in its entirety.

BACKGROUND

The inventive concept relates to a semiconductor process modeling systemand method, and more particularly, to a semiconductor process modelingsystem and method including a preprocessing component and method.

By measuring process parameters using sensors in a semiconductormanufacturing process, raw data may be generated. By monitoring such rawdata, malfunction of semiconductor manufacturing equipment may bedetected, and by modeling the semiconductor process using the raw data,process result values may be predicted. However, due to differentprocess parameter measurement regulations of sensors in semiconductormanufacturing equipment, when the raw data is expressed as a matrixrepresenting values of a plurality of process parameters for each wafer,multiple elements of the matrix may be omitted. A model generated basedon raw data having omitted elements may have a low accuracy.

SUMMARY

The inventive concept provides a semiconductor process modeling systemand method that facilitates easy and accurate process modeling, and asemiconductor manufacturing system including the semiconductor processmodeling system.

According to an aspect of the inventive concept, there is provided asemiconductor process modeling system including a preprocessingcomponent configured to generate tensor data from raw data obtained fromsemiconductor manufacturing equipment, wherein, when the raw data isexpressed as a raw matrix representing values of a plurality of processparameters for each of a plurality of wafers, at least one element ofthe raw matrix is omitted, wherein, when the tensor data is expressed asa tensor matrix representing values of a plurality of preprocessedprocess parameters for each of the plurality of wafers, the number ofomitted elements of the tensor matrix is less than the number of omittedelements of the raw matrix, and wherein the preprocessing component isconfigured to generate the tensor data by modifying the raw data basedon at least one of characteristics of the semiconductor manufacturingequipment and characteristics of the plurality of process parameters.

According to another aspect of the inventive concept, there is provideda semiconductor manufacturing system including: semiconductormanufacturing equipment configured to process a plurality of wafers; anda semiconductor process modeling system, wherein the semiconductorprocess modeling system includes: a preprocessing component configuredto generate tensor data from raw data obtained from the semiconductormanufacturing equipment; and a modeling component configured to model asemiconductor process by using the tensor data, wherein, when the rawdata is expressed as a raw matrix representing values of a plurality ofprocess parameters for each of the plurality of wafers, at least oneelement of the raw matrix is omitted, and wherein, when the tensor datais expressed as a tensor matrix representing values of a plurality ofpreprocessed process parameters for each of the plurality of wafers, thenumber of omitted elements of the tensor matrix is less than the numberof omitted elements of the raw matrix, and wherein the preprocessingcomponent is configured to generate the tensor data by modifying the rawdata based on at least one of characteristics of the semiconductormanufacturing equipment and characteristics of the plurality of processparameters.

According to another aspect of the inventive concept, there is provideda semiconductor process modeling method, the method including: obtainingraw data including values of a plurality of process parameters fromsemiconductor manufacturing equipment; and generating tensor data bymodifying the raw data based on at least one of characteristics of thesemiconductor manufacturing equipment and characteristics of theplurality of process parameters, wherein when the raw data is expressedas a raw matrix representing values of a plurality of process parametersfor each of a plurality of wafers, at least one element of the rawmatrix is omitted, and wherein, when the tensor data is expressed as atensor matrix representing values of a plurality of preprocessed processparameters for each of the plurality of wafers, the number of omittedelements of the tensor matrix is less than the number of omittedelements of the raw matrix.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the inventive concept will be more clearly understoodfrom the following detailed description taken in conjunction with theaccompanying drawings in which like numerals correspond to like elementsthroughout. In the drawings:

FIG. 1 is a block diagram of a semiconductor manufacturing system,according to example embodiments;

FIG. 2 is a diagram of raw data, according to example embodiments;

FIG. 3 is a diagram of tensor data, according to example embodiments;

FIG. 4 is a diagram of tensor data, according to example embodiments;

FIG. 5 is a block diagram of a computer system, according to exampleembodiments;

FIG. 6 is a block diagram of a computer system accessing acomputer-readable medium, according to example embodiments;

FIG. 7 is a diagram of operations of a semiconductor manufacturingsystem, according to example embodiments;

FIG. 8 is a diagram of raw data generated by the operations of FIG. 7 ;

FIG. 9 is a diagram of tensor data generated by the operations of FIG. 7;

FIG. 10 is a diagram of operations of a semiconductor manufacturingsystem, according to example embodiments;

FIG. 11 is a diagram of raw data generated by the operations of FIG. 10;

FIG. 12 is a diagram of tensor data generated by the operations of FIG.10 ;

FIG. 13 is a diagram of operations of a semiconductor manufacturingsystem, according to example embodiments;

FIG. 14 is a diagram of raw data generated by the operations of FIG. 13;

FIG. 15 is a diagram of tensor data generated by the operations of FIG.13 ;

FIG. 16 is a diagram of operations of a semiconductor manufacturingsystem, according to example embodiments;

FIG. 17 is a diagram of raw data generated by the operations of FIG. 16;

FIG. 18 is a diagram of tensor data generated by the operations of FIG.14 ;

FIG. 19 is a block diagram of modeling components, according to exampleembodiments;

FIG. 20 is a conceptual diagram of operations of a modeling component,according to example embodiments;

FIG. 21 is a conceptual diagram of operations of a modeling component,according to example embodiments;

FIG. 22 is a conceptual diagram of operations of a modeling component,according to example embodiments;

FIG. 23 is a diagram of modeling results, according to a comparativeexample;

FIG. 24 is a diagram of modeling results, according to an exampleembodiment;

FIG. 25 is a flowchart of a semiconductor process modeling method,according to example embodiments;

FIG. 26 is a flowchart of a semiconductor process modeling method,according to example embodiments;

FIG. 27 is a flowchart of a semiconductor process modeling method,according to example embodiments;

FIG. 28 is a flowchart of a semiconductor process modeling method,according to example embodiments;

FIG. 29 is a flowchart of a semiconductor process modeling method,according to example embodiments;

FIG. 30 is a flowchart of a semiconductor process modeling method,according to example embodiments; and

FIG. 31 is a flowchart of a semiconductor process modeling method,according to example embodiments.

DETAILED DESCRIPTION OF THE EMBODIMENTS

FIG. 1 is a block diagram of a semiconductor manufacturing system 1000according to example embodiments.

With reference to FIG. 1 , the semiconductor manufacturing system 1000according to example embodiments may include first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h and asemiconductor process modeling system MS. Although FIG. 1 illustratesthat the semiconductor manufacturing system 1000 includes eightmanufacturing equipment, i.e., the first to eighth semiconductormanufacturing equipment 1100 a to 1100 h, the number of semiconductormanufacturing equipment may be any natural number. The first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h may exemplifynumerous semiconductor manufacturing equipment used in a semiconductorprocess.

In some embodiments, the first semiconductor manufacturing equipment1100 a may include etching equipment. The first semiconductormanufacturing equipment 1100 a may be configured to remove at least someportion of a wafer or a material layer on a wafer. The firstsemiconductor manufacturing equipment 1100 a may include at least one ofdry etching equipment and wet etching equipment.

In some embodiments, the second semiconductor manufacturing equipment1100 b may include photolithography equipment. The second semiconductormanufacturing equipment 1100 b may be configured to form a photoresistpattern on a wafer. For example, the second semiconductor manufacturingequipment 1100 b may form a photoresist layer on a wafer, partiallyexpose the photoresist layer to light, and partially remove thephotoresist layer. The second semiconductor manufacturing equipment 1100b may include at least one of photoresist coating equipment (e.g., spincoating equipment), light exposure equipment, and development equipment.

In some embodiments, the third semiconductor manufacturing equipment1100 c may include cleaning equipment. The third semiconductormanufacturing equipment 1100 c may be configured to remove residues orpollutants on a wafer or a material layer on a wafer. The thirdsemiconductor manufacturing equipment 1100 c may include at least one ofwet cleaning equipment, dry cleaning equipment, and steam cleaningequipment.

In some embodiments, the fourth semiconductor manufacturing equipment1100 d may include chemical vapor deposition (CVD) equipment. The fourthsemiconductor manufacturing equipment 1100 d may be configured to form amaterial layer on a wafer by using a CVD method. The fourthsemiconductor manufacturing equipment 1100 d may include at least one ofthermo-CVD equipment, plasma CVD equipment, and photo-CVD equipment.Although not illustrated, in addition to the chemical vapor deposition(CVD) equipment included in the fourth semiconductor manufacturingequipment 1100 d, the fourth semiconductor manufacturing equipment 1100d may further include at least one of physical vapor deposition (PVD)equipment, atomic layer deposition (ALD) equipment, and electricalplating equipment.

In some embodiments, the fifth semiconductor manufacturing equipment1100 e may include chemical physical polish (CMP) equipment. The fifthsemiconductor manufacturing equipment 1100 e may planarize or remove awafer or a material layer on a wafer by polishing the wafer or thematerial layer on the wafer.

In some embodiments, the sixth semiconductor manufacturing equipment1100 f may include ion implant equipment. The sixth semiconductormanufacturing equipment 1100 f may be configured to inject impurity ionsinto a wafer or a material layer on a wafer. The impurity ions mayinclude at least one of Group 15 elements and Group 13 elements. TheGroup 15 elements may include phosphorus (P), arsenic (AS), orcombinations thereof. The Group 13 elements may include boron (B).

In some embodiments, the seventh semiconductor manufacturing equipment1100 g may include diffusion equipment. The seventh semiconductormanufacturing equipment 1100 g may be configured to diffuse impurityions in a wafer or a material layer on a wafer.

In some embodiments, the eighth semiconductor manufacturing equipment1100 h may include metallization equipment. The eighth semiconductormanufacturing equipment 1100 h may be configured to form a metal wire ona wafer.

Each of the first to eighth semiconductor manufacturing equipment 1100 ato 1100 h may sequentially process wafers. The first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h may include atleast one sensor measuring at least one process parameter. For example,each of the first to eighth semiconductor manufacturing equipment 1100 ato 1100 h may include at least one of a temperature sensor, a pressuresensor, a flux sensor, a humidity sensor, a pH sensor, a positionsensor, a power sensor, a voltage sensor, and a current sensor.

The semiconductor process modeling system MS may be configured togenerate tensor data TD from raw data RD including values of a pluralityof process parameters obtained from sensors of the first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h, and model asemiconductor process based on the tensor data TD. The semiconductorprocess modeling system MS may include a preprocessing component 1200and a modeling component 1300 executed by a computer system.

The preprocessing component 1200 may be configured to generate tensordata TD from raw data RD obtained from the first to eighth semiconductormanufacturing equipment 1100 a to 1100 h. The preprocessing component1200 may be configured to generate tensor data TD by modifying raw dataRD based on at least one of characteristics of the first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h andcharacteristics of a plurality of process parameters.

The modeling component 1300 may model a semiconductor process to predicta process result value based on the tensor data TD. Here, the processresult may be, for example, a yield, width of pattern, length ofpattern, diameter of pattern, diameter of hole, depth of hole, standarddeviation of dimension of a pattern, etc. In some embodiments, machinelearning may be used in semiconductor process modeling. In such cases,the modeling component 1300 may train a machine learning model forprediction of process result values based on the tensor data TD.

A user UR may control, change, and/or adjust at least one of the firstto eighth semiconductor manufacturing equipment 1100 a to 1100 h basedon a model generated by the modeling component 1300 of the semiconductorprocess modeling system MS. For example, the user UR may control,change, and/or adjust at least one of the first to eighth semiconductormanufacturing equipment 1100 a to 1100 h to achieve a desired processresult value. For example, to improve a yield the user UR may find aprocess parameter which most greatly affects the yield, and thencontrol, change, and/or adjust at least one of the first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h to change theprocess parameter.

FIG. 2 is a diagram of raw data RD according to example embodiments.

With reference to FIG. 2 , the raw data RD may be expressed as a rawmatrix representing values of a plurality of process parameters P foreach of a plurality of wafers WF (e.g., first to fourth wafers WF1 toWF4) and a lot WF0, which may include the first to fourth wafers WF1 toWF4. The values of the process parameters P may include, for example,temperatures T11, T12, T2, and T3, a thickness t4, and a thicknessdifference Δt4. Although not illustrated, the process parameters P mayfurther include a pressure, flux rate, pH, humidity, illuminance, time,voltage, power, current, etc. As shown in FIG. 2 , some elements FC of araw matrix may have a value while other elements EC of the raw matrixmay not have a value. That is, some elements FC of the raw matrix may befilled while other elements EC of the raw matrix may be omitted.

When a constant value, e.g., 0, is arbitrarily inserted into omitteddata, or modeling is carried out only with filled data FC, the modelingis performed based on distorted data, which may lead to performancedegradation of a semiconductor process model. To fill data with ameaningful value, understanding of characteristics of equipment to whichmeasured parameters pertain and characteristics of the measuredparameters is required. Thus, performing modeling by using such raw dataRD in equipment may not be easy to non-experts.

FIG. 3 is a diagram of tensor data TD according to example embodiments.

With reference to FIG. 3 , the tensor data TD may be expressed as atensor matrix representing values of a plurality of preprocessed processparameters P′ for each of a plurality of wafers WF (e.g., first tofourth wafers W1 to W4). The values of the preprocessed processparameters P′ may be calculated from values of the process parameters Pof the raw data RD. Some elements FC′ of the tensor matrix may have avalue while other elements EC′ of the tensor matrix may not have a valueas shown in FIG. 3 . For example, some elements FC′ of the tensor matrixmay be filled while other elements EC′ of the tensor matrix may beomitted. However, the number of omitted elements EC′ of the tensormatrix may be less than the number of omitted elements EC of the rawmatrix RD of FIG. 2 . For example, the number of omitted elements EC′ ofthe tensor matrix of FIG. 3 is 3, and the number of omitted elements ECof the raw matrix of FIG. 2 is 16.

Among the plurality of preprocessed process parameters P′, thepreprocessed process parameters T1, T3, and t4 having a correspondingvalue for each of the wafers WF may be defined as being tensorized. Onthe other hand, some parameters T2 and Δt4 of the plurality ofpreprocessed process parameters P′ may not be tensorized. Thetensorization rate may be defined as “(the number of tensorizedpreprocessed process parameters)/(the number of all preprocessed processparameters)×100.” In the example of FIG. 3 , the tensorization rate is(3/5)×100=60%. When modeling of a semiconductor process is performedbased on the tensor data TD, performance of the semiconductor processmodel may be improved. For example, a model may better predict a processresult value from at least one of a plurality of preprocessed processparameters P′.

FIG. 4 is a diagram of tensor data TD0 according to example embodiments.

With reference to FIG. 4 , the tensor data TD0 may be expressed as atensor matrix representing values of a plurality of preprocessed processparameters P0′ for each of a plurality of wafers WF (e.g., first tofourth wafers W1 to W4). All elements of the tensor matrix may befilled. That is, the number of omitted elements of the tensor matrix maybe 0. In other words, the tensor matrix may not include an omittedelement. For example, the tensor data TD0 may be completely tensorized,and the tensorization rate of the tensor data TD0 may be 100%. Whenmodeling of a semiconductor process is performed based on the tensordata TD0, performance of the model may be improved. For example, a modelmay better predict a process result value from at least one of aplurality of preprocessed process parameters P0′. As there is no omittedelement, non-experts may also easily perform modeling of thesemiconductor process by using the tensor data TD0 and the modelingcomponent 1300 (see FIG. 1 ).

FIG. 5 is a block diagram of a computer system 170 according to exampleembodiments. A semiconductor process modeling method, which is describedwith reference to FIGS. 25 to 31 , may be performed in the computersystem 170. In some embodiments, the computer system 170 may be referredto as a semiconductor process modeling system MS (see FIG. 1 ).

The computer system 170 may include at least one computing device. Forexample, the computer system 170 may include a first computing devicewhere the preprocessing component 1200 of FIG. 1 is executed and asecond computing device where the modeling component 1300 of FIG. 1 isexecuted. In another embodiment, the preprocessing component 1200 andthe modeling component 1300 may be executed in the same computingdevice. The computing device may be a fixed computing device, such as adesktop computer, a workstation, a server, etc., or may be a portablecomputing device, such as a laptop computer, a tablet, a smartphone,etc.

As shown in FIG. 5 , the computer system 170 may include a processor171, input/output (I/O) devices 172, a network interface 173, randomaccess memory (RAM) 174, read only memory (ROM) 175, and a storage 176.The processor 171, the I/O devices 172, the network interface 173, theRAM 174, the ROM 175, and the storage 176 may be connected to a bus 177,and communicate with each other through the bus 177.

The processor 171 may be referred to as a processing unit, and mayinclude at least one core capable of executing a command set (e.g.,Intel Architecture (IA)-32, 64 bit extension IA-32, x86-64, PowerPC,Sparc, MIPS, ARM, IA-64, etc.), such as a micro-processor, anapplication processor (AP), a digital signal processor (DSP), and agraphics processing unit (GPU). For example, the processor 171 mayaccess the memory, i.e., RAM 174, or ROM 175 through the bus 177, andexecute commands stored in the RAM 174 or ROM 175.

The RAM 174 may store a program 174_1 for semiconductor process modelingor at least a portion thereof, and the program 174_1 for semiconductorprocess modeling may make the processor 171 perform a semiconductorprocess modeling method. For example, the program 174_1 may include aplurality of commands executable by the processor 171, and the pluralityof commands included in the program 174_1 may make the processor 171perform a semiconductor process modeling method.

The storage 176 may not lose stored data even when the power supplied tothe computer system 170 is cut. For example, the storage 176 may includea non-volatile memory device, or may include a storage medium such as amagnetic tape, an optical disk, and a magnetic disk. Further, thestorage 176 may be removable from the computer system 170. The storage176 may store the program 174_1 according to an example embodiment ofthe inventive concept, and the program 174_1 or at least a portionthereof may be loaded to the RAM 174 from the storage 176 before theprogram 174_1 is executed by the processor 171. Alternatively, thestorage 176 may store a file written in a program language, and theprogram 174_1 generated by a compiler, etc. or at least a portionthereof may be loaded to the RAM 174 from the file. As shown in FIG. 5 ,the storage 176 may store a database 176_1, and the database 176_1 mayinclude data required for semiconductor process modeling, for example,the raw data RD of FIG. 1 .

The storage 176 may store data to be processed by the processor 171 ordata processed by the processor 171. For example, the processor 171 maygenerate data by processing data stored in the storage 176 according tothe program 174_1, and store the generated data, for example, the tensordata TD of FIG. 1 and predictive values of a process result in thestorage 176.

The I/O devices 172 may include an input device such as a keyboard, apointing device, etc., and may include an output device such as adisplay device, a printer, etc. For example, a user may triggerexecution of the program 174_1 by the processor 171 through the I/Odevices 172, and check the resulting data.

The network interface 173 may provide access to a network outside thecomputer system 170. For example, a network may include multiplecomputing systems and communication links, and the communication linksmay include wired links, optical links, wireless links, or any othertypes of links.

FIG. 6 is a block diagram of a computer system 182 accessing acomputer-readable medium 184 according to example embodiments. At leastsome of the operations included in the semiconductor process modelingmethod shown in FIGS. 25 to 31 may be performed by the computer system182. The computer system 182 may access the computer-readable medium 184and may execute a program 184_1 stored in the computer-readable medium184. In some embodiments, the computer system 182 and thecomputer-readable medium 184 may be collectively referred to as asemiconductor process modeling system MS (see FIG. 1 ).

The computer system 182 may include at least one computer subsystem, andthe program 184_1 may include at least one component executed by atleast one computer subsystem. For example, at least one component mayinclude the preprocessing component 1200 (see FIG. 1 ) and the modelingcomponent 1300 (see FIG. 1 ). Similar to the storage 176 of FIG. 5 , thecomputer-readable medium 184 may include a non-volatile memory device,or a storage medium such as a magnetic tape, an optical disk, and amagnetic disk. Further, the computer-readable medium 184 may beremovable from the computer system 182.

FIG. 7 is a diagram of operations of a semiconductor manufacturingsystem 1000-1 according to example embodiments. FIG. 8 is a diagram ofraw data RD1 generated by the operations of FIG. 7 . FIG. 9 is a diagramof tensor data TD1 generated by the operations of FIG. 7 .

With reference to FIGS. 7 to 9 , semiconductor manufacturing equipment1100-1 may include a first chamber CH1 and a second chamber CH2. Thesemiconductor manufacturing equipment 1100-1 may process some of thefirst to fourth wafers WF1 to WF4, for example, the first wafer WF1 andthe third wafer WF3, in the first chamber CH1. The semiconductormanufacturing equipment 1100-1 may process some of the first to fourthwafers WF1 to WF4, for example, the second wafer WF2 and the fourthwafer WF4, in the second chamber CH2. The semiconductor manufacturingequipment 1100-1 may be any one of the first to eighth semiconductormanufacturing equipment 1100 a through 1100 h of FIG. 1 .

The preprocessing component 1200 may obtain a value of a first processparameter T11 from the first chamber CH1 of the semiconductormanufacturing equipment 1100-1 in which the first wafer WF1 and thethird wafer WF3 are sequentially processed. Further, the preprocessingcomponent 1200 may obtain a value of a second process parameter T12 fromthe second chamber CH2 of the semiconductor manufacturing equipment1100-1 in which the second wafer WF2 and the fourth wafer WF4 aresequentially processed. For example, the first process parameter T11 maybe a temperature of the first chamber CH1, and the second processparameter T12 may be a temperature of the second chamber CH2.

In this case, the raw data RD1 may include the value of the firstprocess parameter T11 for each of the first wafer WF1 and the thirdwafer WF3, and the value of the second process parameter T12 for each ofthe second wafer WF2 and the fourth wafer WF4. On the contrary, the rawdata RD1 may not include the value of the second process parameter T12for each of the first wafer WF1 and the third wafer WF3, and the valueof the first process parameter T11 for each of the second wafer WF2 andthe fourth wafer WF4.

The preprocessing component 1200 may generate the tensor data TD1 bymerging the first process parameter T11 and the second process parameterT12 into one preprocessed process parameter T1. For example, a value ofthe preprocessed process parameter T1 for the first wafer WF1 may beidentical to a value of the first process parameter T11 for the firstwafer WF1, a value of the preprocessed process parameter T1 for thesecond wafer WF2 may be identical to a value of the second processparameter T12 for the second wafer WF2, a value of the preprocessedprocess parameter T1 for the third wafer WF3 may be identical to a valueof the first process parameter T11 for the third wafer WF3, and a valueof the preprocessed process parameter T1 for the fourth wafer WF4 may beidentical to a value of the second process parameter T12 for the fourthwafer WF4. The preprocessing component 1200 may provide the generatedtensor data TD1 to the modeling component 1300 for further processing.

FIG. 10 is a diagram of operations of a semiconductor manufacturingsystem 1000-2 according to example embodiments. FIG. 11 is a diagram ofraw data RD2 generated by the operations of FIG. 10 . FIG. 12 is adiagram of tensor data TD2 generated by the operations of FIG. 10 .

The semiconductor manufacturing equipment 1100-2 may include a chamberCH-2. The chamber CH-2 may accommodate two wafers at the same time. Thesemiconductor manufacturing equipment 1100-2 may simultaneously processthe first wafer WF1 and the second wafer WF2 in the chamber CH-2.Further, the semiconductor manufacturing equipment 1100-2 maysimultaneously process the third wafer WF3 and the fourth wafer WF4 inthe chamber CH-2. The semiconductor manufacturing equipment 1100-2 maybe any one of the first to eighth semiconductor manufacturing equipment1100 a through 1100 h of FIG. 1 .

The preprocessing component 1200 may obtain the value of the processparameter T2 from the chamber CH-2. In some embodiments, the processparameter T2 may be a temperature of the chamber CH-2.

In this case, the raw data RD2 may include a value of the processparameter T2 for the first wafer WF1, not include a value of the processparameter T2 for the second wafer WF2, include a value of the processparameter T2 for the third wafer WF3, and not include a value of theprocess parameter T2 for the fourth wafer WF4.

The preprocessing component 1200 may generate the tensor data TD2 byreplicating the value of the process parameter T2 for the first waferWF1 as a value of a preprocessed process parameter T2′ for each of thefirst wafer WF1 and the second wafer WF2, and replicating the value ofthe process parameter T2 for the third wafer WF3 as a value of apreprocessed process parameter T2′ for each of the third wafer WF3 andthe fourth wafer WF4. For example, the value of the preprocessed processparameter T2′ for each of the first wafer WF1 and the second wafer WF2may be identical to the value of the process parameter T2 for the firstwafer WF1, and the value of the preprocessed process parameter T2′ foreach of the third wafer WF3 and the fourth wafer WF4 may be identical tothe value of the process parameter T2 for the third wafer WF3. Thepreprocessing component 1200 may provide the generated tensor data TD2to the modeling component 1300 for further processing.

FIG. 13 is a diagram of operations of a semiconductor manufacturingsystem 1000-3 according to example embodiments. FIG. 14 is a diagram ofraw data RD3 generated by the operations of FIG. 13 . FIG. 15 is adiagram of tensor data TD3 generated by the operations of FIG. 13 .

With reference to FIGS. 13 to 15 , the semiconductor manufacturingequipment 1100-3 may include a chamber CH-3, and the semiconductormanufacturing equipment 1100-3 may process a lot WF0 including the firstto fourth wafers WF1 to WF4 in the chamber CH-3. For example, thesemiconductor manufacturing equipment 1100-3 may simultaneously processthe first to fourth wafers WF1 to WF4 in the chamber CH-3. Thesemiconductor manufacturing equipment 1100-3 may be any one of the firstto eighth semiconductor manufacturing equipment 1100 a through 1100 h ofFIG. 1 .

The preprocessing component 1200 may obtain a value of the processparameter T3 from the chamber CH-3 of the semiconductor manufacturingequipment 1100-3 in which the lot WF0 is processed. Here, the processparameter T3 may be a temperature of the chamber CH-3.

In this case, the raw data RD3 may include a value of the processparameter T3 for the lot WF0 and may not include a value of the processparameter T3 for the first to fourth wafers WF1 to WF4.

The preprocessing component 1200 may generate the tensor data TD3 byreplicating the value of the process parameter T3 for the lot WF0 as avalue of a preprocessed process parameter T3′ for each of the first tofourth wafers WF1 to WF4. For example, the value of the preprocessedprocess parameter T3′ for each of the first to fourth wafers WF1 to WF4may be identical to the value of the process parameter T3 for the lotWF0. The preprocessing component 1200 may provide the generated tensordata TD3 to the modeling component 1300 for further processing.

Although FIGS. 13-15 illustrate a lot including four wafers (e.g., firstto fourth wafers WF1 to WF4), the number of wafers in a lot may begreater or fewer. For example, lot WF0 may include two wafers (e.g.,first and second wafer WF1 and WF2), three wafers (e.g., first throughthird wafers WF1 to WF3), or more than four wafers (e.g., first waferWF1 through n-th wafer WFn).

FIG. 16 is a diagram of operations of a semiconductor manufacturingsystem 1000-4 according to example embodiments. FIG. 17 is a diagram ofraw data RD4 generated by the operations of FIG. 16 . FIG. 18 is adiagram of tensor data TD 4 generated by the operations of FIG. 14 .

With reference to FIGS. 16 to 18 , the semiconductor manufacturingequipment 1100-4 may sequentially process the first to fourth wafers WF1to WF4. The semiconductor manufacturing equipment 1100-4 may be any oneof the first to eighth semiconductor manufacturing equipment 1100 athrough 1100 h of FIG. 1 . The preprocessing component 1200 may obtain afirst process parameter t4 and a second process parameter Δt4 from thesemiconductor manufacturing equipment 1100-3. The first processparameter t4 may be a thickness of a thin film on a wafer, and thesecond process parameter Δt4 may be a thickness difference between athin film of the first wafer WF1 and a thin film of a certain waferother than the first wafer WF1.

The raw data RD4 may include a value of the first process parameter t4for the first wafer WF1, but not include a value of the second processparameter Δt4 for the first wafer WF1, and include a value of the firstprocess parameter t4 and the second process parameter Δt4 for the secondwafer WF2, a value of the first process parameter t4 and the secondprocess parameter Δt4 for the third wafer WF3, and a value of the firstprocess parameter t4 and the second process parameter Δt4 for the fourthwafer WF4. For example, when the raw data RD4 is expressed as a rawmatrix, an element corresponding to the value of the second processparameter Δt4 for the first wafer WF1 may be omitted.

The values of the second process parameter Δt4 for the second to fourthwafers WF2 to WF4 may be calculated from the values of the first processparameter t4 for the first to fourth wafers WF1 to WF4. For example,when the first process parameter t4 is a thickness of a thin film on awafer, and the second process parameter Δt4 is a thickness differencebetween a thin film on the first wafer WF1 and a thin film on a certainwafer, the value of the second process parameter Δt4 for the secondwafer WF2 may be calculated by subtracting the value of the firstprocess parameter t4 for the first wafer WF1 from the value of the firstprocess parameter t4 for the second wafer WF2. Similarly, the value ofthe second process parameter Δt4 for the third wafer WF3 may becalculated by subtracting the value of the first process parameter t4for the first wafer WF1 from the value of the first process parameter t4for the third wafer WF3. Also, the value of the second process parameterΔt4 for the fourth wafer WF4 may be calculated by subtracting the valueof the first process parameter t4 for the first wafer WF1 from the valueof the first process parameter t4 for the fourth wafer WF4.

The preprocessing component 1200 may generate the tensor data TD4 bydeleting the value of the second process parameter Δt4 for the secondwafer WF2. For example, the tensor data TD4 may include the value of thefirst process parameter t4 for each of the first to fourth wafers WF1 toWF4, and may not include the value of the second process parameter Δt4for any of the first to fourth wafers WF1 to WF4. The preprocessingcomponent 1200 may provide the generated tensor data TD4 to the modelingcomponent 1300 for further processing.

FIGS. 7 to 18 illustrate examples in which when raw data is expressed asa raw matrix, the raw matrix has omitted elements, and examples in whichtensor data is generated from raw data based on at least one ofcharacteristics of semiconductor manufacturing equipment andcharacteristics of parameters. However, there may be various examples inwhich when raw data is expressed as a raw matrix, the raw matrix hasomitted elements, in addition to the examples illustrated in FIGS. 7 to18 . Further, there may be various examples in which tensor data isgenerated from raw data based on at least one of characteristics ofsemiconductor manufacturing equipment and characteristics of parameters,in addition to the examples illustrated in FIGS. 7 to 18 .

FIG. 19 is a block diagram of a modeling component 1300 according toexample embodiments. FIG. 20 is a conceptual diagram of operations of amodeling component 1300 according to example embodiments. FIG. 21 is aconceptual diagram of operations of a modeling component 1300 accordingto example embodiments. FIG. 22 is a conceptual diagram of operations ofa modeling component 1300 according to example embodiments.

With reference to FIGS. 19 to 22 , the modeling component 1300 mayinclude a model learning subcomponent 1310, a process result valueprediction subcomponent 1320, and a variable importance calculationsubcomponent 1330.

The model learning subcomponent 1310 may generate a machine learningmodel MD and train the machine learning model MD. The machine learningmodel MD may include, for example, a linear regression model, a supportvector machine model, a decision tree model, a random forest model, anXG Boost model, or a Gradient Boost model, etc.

The model learning subcomponent 1310 may train the machine learningmodel MD by using supervised learning, semi-supervised learning,unsupervised learning, or combinations thereof. The model learningsubcomponent 1310 may be trained to output a process result predictivevalue from at least one preprocessed process parameter.

The process result value prediction subcomponent 1320 may predict aprocess result value from at least one preprocessed process parameter byusing the machine learning model MD trained by the model learningsubcomponent 1310 as shown in FIG. 20 .

The variable importance calculation subcomponent 1330 may calculateimportance of each preprocessed process parameter from a first machinelearning model MD1 trained to predict a process result predictive valuefrom a plurality of preprocessed process parameters by using the firstmachine learning model MD1 trained by the model learning subcomponent1310 as shown in FIG. 21 . A preprocessed process parameter of highimportance may have a greater effect on a process result value.

In addition, the model learning subcomponent 1310 may train a secondmachine learning model MD2 to predict a process result value from apreprocessed process parameter having the highest importance among theplurality of preprocessed process parameters. The process result valueprediction subcomponent 1320 may predict a process result value from apreprocessed process parameter having the highest importance by usingthe second machine learning model MD2 trained by the model learningsubcomponent 1310 as shown in FIG. 22 .

FIG. 23 is a diagram of modeling results according to a comparativeexample.

With reference to FIG. 23 , the process result value is predicted byusing a machine learning model trained based on raw data withoutconverting the raw data into the tensor data. The XGBoost model has beenused as a machine running model. In FIG. 23 , the X axis represents apredictive value of a process result, and the Y axis represents anactual value of the process result. The R² value representing thecorrelation between the predictive value and the actual value of theprocess result has been calculated as −0.11. The R² having a negativevalue means that there is no correlation between the predictive valueand the actual value of the process result. For example, a machinelearning model trained based on raw data without converting the raw datainto tensor data may not predict process result values accurately.

FIG. 24 is a diagram of modeling results according to an exampleembodiment.

With reference to FIG. 24 , a process result value is predicted by usinga machine learning model trained based on the tensor data. The XGBoostmodel has been used as a machine running model. In FIG. 24 , the X axisrepresents a predictive value of a process result, and the Y axisrepresents an actual value of the process result. The R² valuerepresenting the correlation between the predictive value and the actualvalue of the process result has been calculated as 0.37. Such valueindicates that there is significant correlation between the predictivevalue and the actual value of the process result. For example, a machinelearning model trained based on the tensor data has successfullypredicted a process result value. Upon comparing the comparative exampleof FIG. 23 to the embodiment of FIG. 24 , it is understood that a usermay obtain a high performance model more easily through thesemiconductor process modeling system converting the raw data into thetensor data.

FIG. 25 is a flowchart of a semiconductor process modeling method 100according to example embodiments.

With reference to FIGS. 25 and FIGS. 1-3 , the raw data RD includingvalues of a plurality of process parameters may be obtained from thefirst to eighth semiconductor manufacturing equipment 1100 a to 1100 h(S110). Then, the tensor data TD may be generated by modifying the rawdata RD based on at least one of characteristics of the first to eighthsemiconductor manufacturing equipment 1100 a to 1100 h andcharacteristics of the plurality of process parameters (S120). Next,modeling may be performed based on the tensor data TD (S130).

FIG. 26 is a flowchart of a semiconductor process modeling method 100-1according to example embodiments.

With reference to FIGS. 26 and FIGS. 7-9 , operation S110-1 foracquiring the raw data may include operation S110-1 a for obtaining avalue of the first process parameter T11 for the first wafer WF1 fromthe first chamber CH1 of the semiconductor manufacturing equipment1100-1, and operation S110-1 b for obtaining a value of the secondprocess parameter T12 for the second wafer WF2 from the second chamberCH2 of the semiconductor manufacturing equipment in which the secondwafer WF2 is processed. In some embodiments, operation S110-1 a forobtaining the value of the first process parameter T11 and the operationS110-1 b for obtaining the value of the second process parameter T12 maybe performed simultaneously. Next, the tensor data TD1 may be generatedby merging the first process parameter T11 and the second processparameter T12 into a preprocessed process parameter (S120-1). Then,modeling may be performed based on the tensor data TD1 (S130).

FIG. 27 is a flowchart of a semiconductor process modeling method 100-2according to example embodiments.

With reference to FIGS. 27 and FIGS. 10-12 , the raw data may beobtained by obtaining a value of a process parameter for the first waferWF1 from the chamber CH-2 of the semiconductor manufacturing equipment1100-2 in which the first wafer WF1 and the second wafer WF2 areprocessed simultaneously (S110-2). Next, the tensor data TD2 may begenerated by replicating a value of the process parameter T2 for thefirst wafer WF1 as a value of the preprocessed process parameter T2′ foreach of the first wafer WF1 and the second wafer WF2 (S120-2). Then,modeling may be performed based on the tensor data TD2 (S130). FIG. 28is a flowchart of a semiconductor process modeling method 100-3according to example embodiments.

With reference to FIGS. 28 and FIGS. 13-15 , the raw data may beobtained by obtaining a value of the process parameter T3 from thechamber CH-3 of the semiconductor manufacturing equipment 1100-3 inwhich the lot WF0 including the first through fourth wafers WF1 to WF4is processed (S110-3). Next, the tensor data TD3 may be generated byreplicating a value of the process parameter T3 for the lot WF0 as avalue of the preprocessed process parameter T3′ for each of the firstthrough fourth wafers WF1 to WF4. Then, modeling may be performed basedon the tensor data TD3 (S130).

FIG. 29 is a flowchart of a semiconductor process modeling method 100-4according to example embodiments.

With reference to FIGS. 29 and FIGS. 16-18 , operation S110-4 to obtainthe raw data may include operation S110-4 a to obtain a value of thefirst process parameter t4 for the first wafer WF1 and operation S110-4b to obtain a value of the first process parameter t4 and the secondprocess parameter Δt4 for the second wafer WF2. Next, the tensor dataTD4 may be generated by deleting the second process parameter Δt4 forthe second wafer WF2 (S120-4). Then, modeling may be performed based onthe tensor data TD4 (S130).

In some embodiments, operation S110-4 b may be performed for the thirdwafer WF3 and the fourth wafer WF4. For example, in operation S110-4 b,values of the first process parameter t4 and the second processparameter Δt4 for the second through fourth wafers WF2 to WF4 may beobtained. In such embodiments, in operation S120-4, the tensor data TD4may be generated by deleting the second process parameters Δt4 for eachof the second through fourth wafers WF2 to WF4.

FIG. 30 is a flowchart of a semiconductor process modeling method 100-5according to example embodiments.

With reference to FIGS. 30 and 20 , the raw data may be obtained (S110)and the tensor data may be generated from the raw data (S120). Next, themodeling operation S130-5 may include operation S130-5 a for trainingthe machine learning model MD to predict a process result value from atleast one preprocessed process parameter and operation S130-5 b forpredicting a process result value from at least one preprocessed processparameter by using the machine learning model MD.

FIG. 31 is a flowchart of a semiconductor process modeling method 100-6according to example embodiments.

With reference to FIGS. 31, 21, and 22 , the raw data may be obtained(S110) and the tensor data may be generated from the raw data (S120).Next, the modeling operation S130-6 may include operation S130-6 a fortraining the first machine learning model MD1 to predict a processresult value from a plurality of preprocessed process parameters,operation S130-6 b for calculating importance of the plurality ofpreprocessed process parameters by using the first machine learningmodel MD1, operation S130-6 c for training the second machine learningmodel MD2 to predict a process result value from a preprocessed processparameter having the highest importance among the plurality ofpreprocessed process parameters, and operation S130-6 d for predicting aprocess result value from the preprocessed process parameter having thehighest importance by using the second machine learning model MD2.

While the inventive concept has been particularly shown and describedwith reference to embodiments thereof, it will be understood thatvarious changes in form and details may be made therein withoutdeparting from the spirit and scope of the following claims.

1. A semiconductor process modeling system comprising: a preprocessingcomponent configured to generate tensor data from raw data obtained fromsemiconductor manufacturing equipment, wherein, when the raw data isexpressed as a raw matrix representing values of a plurality of processparameters for each of a plurality of wafers, at least one element ofthe raw matrix is omitted, wherein, when the tensor data is expressed asa tensor matrix representing values of a plurality of preprocessedprocess parameters for each of the plurality of wafers, a number ofomitted elements of the tensor matrix is less than a number of omittedelements of the raw matrix, and wherein the preprocessing component isconfigured to generate the tensor data by modifying the raw data basedon at least one of characteristics of the semiconductor manufacturingequipment and characteristics of the plurality of process parameters. 2.The semiconductor process modeling system of claim 1, wherein the numberof omitted elements of the tensor matrix is
 0. 3. The semiconductorprocess modeling system of claim 1, wherein the raw data includes avalue of a first process parameter for a first wafer and a value of asecond process parameter for a second wafer, and wherein thepreprocessing component is configured to generate the tensor data fromthe raw data so that a value of a preprocessed process parameter for thefirst wafer is identical to the value of the first process parameter forthe first wafer, and a value of the preprocessed process parameter forthe second wafer is identical to the value of the second processparameter for the second wafer.
 4. The semiconductor process modelingsystem of claim 3, wherein the preprocessing component is configured toobtain the value of the first process parameter from a first chamber ofthe semiconductor manufacturing equipment in which the first wafer isprocessed, and obtain the value of the second process parameter from asecond chamber of the semiconductor manufacturing equipment in which thesecond wafer is processed.
 5. The semiconductor process modeling systemof claim 1, wherein the raw data includes a value of a process parameterfor a first wafer, and wherein the preprocessing component is configuredto generate the tensor data from the raw data so that a value of apreprocessed process parameter for each of the first wafer and a secondwafer is identical to the value of the process parameter for the firstwafer.
 6. The semiconductor process modeling system of claim 5, whereinthe preprocessing component is configured to obtain the value of theprocess parameter from a chamber of the semiconductor manufacturingequipment in which the first wafer and the second wafer aresimultaneously processed.
 7. The semiconductor process modeling systemof claim 1, wherein the raw data includes a value of a process parameterfor a lot including a first wafer and a second wafer, and wherein thepreprocessing component is configured to generate the tensor data fromthe raw data so that a value of a preprocessed process parameter foreach of the first wafer and the second wafer is identical to the valueof the process parameter for the lot.
 8. The semiconductor processmodeling system of claim 7, wherein the preprocessing component isconfigured to obtain the value of the process parameter from a chamberof the semiconductor manufacturing equipment in which the lot isprocessed.
 9. The semiconductor process modeling system of claim 1,wherein the raw data includes a value of a first process parameter for afirst wafer and a value of the first process parameter and a secondprocess parameter for a second wafer, and wherein the preprocessingcomponent is configured to generate the tensor data from the raw data sothat the tensor data includes the value of the first process parameterfor each of the first wafer and the second wafer, and omits the value ofthe second process parameter for the second wafer.
 10. The semiconductorprocess modeling system of claim 9, wherein, in the raw data, the valueof the second process parameter for the second wafer is calculated fromthe value of the first process parameter for each of the first wafer andthe second wafer.
 11. The semiconductor process modeling system of claim1, further comprising: a modeling component including a model learningsubcomponent configured to train a first machine learning model topredict a process result value from at least one of the plurality ofpreprocessed process parameters.
 12. The semiconductor process modelingsystem of claim 11, wherein the modeling component further includes avariable importance calculation subcomponent configured to calculateimportance of the plurality of preprocessed process parameters for theprocess result value by using the first machine learning model.
 13. Thesemiconductor process modeling system of claim 12, wherein the modellearning subcomponent is configured to train a second machine learningmodel to predict a process result value from a preprocessed processparameter of highest importance among the plurality of preprocessedprocess parameters.
 14. A semiconductor manufacturing system comprising:semiconductor manufacturing equipment configured to process a pluralityof wafers; and a semiconductor process modeling system, wherein thesemiconductor process modeling system includes: a preprocessingcomponent configured to generate tensor data from raw data obtained fromthe semiconductor manufacturing equipment; and a modeling componentconfigured to model a semiconductor process by using the tensor data,wherein, when the raw data is expressed as a raw matrix representingvalues of a plurality of process parameters for each of the plurality ofwafers, at least one element of the raw matrix is omitted, and wherein,when the tensor data is expressed as a tensor matrix representing valuesof a plurality of preprocessed process parameters for each of theplurality of wafers, a number of omitted elements of the tensor matrixis less than a number of omitted elements of the raw matrix, and whereinthe preprocessing component is configured to generate the tensor data bymodifying the raw data based on at least one of characteristics of thesemiconductor manufacturing equipment and characteristics of theplurality of process parameters.
 15. The semiconductor manufacturingsystem of claim 14, wherein the raw data includes a value of a firstprocess parameter for a first wafer and a value of a second processparameter for a second wafer, and wherein the preprocessing component isconfigured to generate the tensor data by merging the first processparameter and the second process parameter into one preprocessed processparameter.
 16. The semiconductor manufacturing system of claim 15,wherein the semiconductor manufacturing equipment includes a firstchamber and a second chamber, and is configured to process the firstwafer in the first chamber and process the second wafer in the secondchamber, and wherein the preprocessing component is configured to obtaina value of the first process parameter from the first chamber and avalue of the second process parameter from the second chamber.
 17. Thesemiconductor manufacturing system of claim 14, wherein the raw dataincludes a value of a process parameter for a first wafer, and whereinthe preprocessing component is configured to generate the tensor data byreplicating the value of the process parameter for the first wafer as avalue of a preprocessed process parameter for each of the first waferand a second wafer.
 18. (canceled)
 19. The semiconductor manufacturingsystem of claim 14, wherein the raw data includes a value of a processparameter for a lot including a first wafer and a second wafer, andwherein the preprocessing component is configured to generate the tensordata by replicating the value of the process parameter for the lot as avalue of a preprocessed process parameter for each of the first waferand the second wafer.
 20. (canceled)
 21. The semiconductor manufacturingsystem of claim 14, wherein the raw data includes a value of a firstprocess parameter for a first wafer and a value of the first processparameter and a second process parameter for a second wafer, and whereinthe preprocessing component is configured to generate the tensor data bydeleting the value of the second process parameter for the second wafer.22. (canceled)
 23. A semiconductor process modeling method comprising:obtaining raw data including values of a plurality of process parametersfrom semiconductor manufacturing equipment; and generating tensor databy modifying the raw data based on at least one of characteristics ofthe semiconductor manufacturing equipment and characteristics of theplurality of process parameters, wherein, when the raw data is expressedas a raw matrix representing values of the plurality of processparameters for each of a plurality of wafers, at least one element ofthe raw matrix is omitted, and wherein, when the tensor data isexpressed as a tensor matrix representing values of a plurality ofpreprocessed process parameters for each of the plurality of wafers, anumber of omitted elements of the tensor matrix is less than a number ofomitted elements of the raw matrix. 24.-34. (canceled)